The Intersection Exponent for Simple Random Walk

Combinatorics Probability and Computing

Volumn 9, Issue 5, 2000, Pages 441-464

  Lawler, Gregory F ^a   Puckette, Emily E ^b  

^a DUKE UNIVERSITY   (United States)

^b OCCIDENTAL COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034556773     PISSN: 09635483     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0963548300004442     Document Type: Article

References (24)

1. Ahlfors, L. (1973) Conformal Invariants: Topics in Geometric Function Theory, McGraw-Hill.
2. Aizenman, M., Burchard, A., Newman, C. and Wilson, D. (1999) Scaling limits for minimal and random spanning trees in two dimensions. Random Structures and Algorithms 15 319-367.
3. Bass, R. (1995) Probabilistic Techniques in Analysis, Springer.
4. Burdzy, K. and Lawler, G. (1990) Non-intersection exponents for random walk and Brownian motion, Part I: Existence and an invariance principle. Prob. Theor. Rel. Fields 84 393-410.
5. Cardy, J. L. (1998) The number of incipient spanning clusters in two-dimensional percolation. J. Phys. A 31 L105.
6. Cranston, M. and Mountford, T. (1991) An extension of a result of Burdzy and Lawler. Prob. Theor. Rel. Fields 89 487-502.
7. Duplantier, B. (1992) Loop-erased self-avoiding walks in two dimensions: exact critical exponents and winding numbers. Physica A 191 516-522.
8. Duplantier, B. and Kwon, K.-H. (1988) Conformal invariance and intersection of random walks. Phys. Rev. Lett. 61 2514-2517.
9. Duplantier, B. and Saleur, H. (1986) Exact surface and wedge exponents for polymers in two dimensions. Phys. Rev. Lett. 57 3179-3182.
10. Duplantier, B. and Saleur, H. (1987) Exact determination of the percolation hull exponent in two dimensions. Phys. Rev. Lett. 58 2325.
11. Langlands, R., Pouillot, Y. and Saint-Aubin, Y. (1994) Conformal invariance in two-dimensional percolation. Bull. Amer. Math. Soc. 30 1-61.
12. Lawler, G. (1991) Intersections of Random Walks, Birkhäuser, Boston.
13. Lawler, G. (1993) A discrete analogue of a theorem of Makarov. Combin. Probab. Comput. 2 181-199.
14. Lawler, G. (1995) Nonintersecting planar Brownian motions. Math. Phys. Electron. J. 1 #4.
15. Lawler, G. (1996) Hausdorff dimension of cut points for Brownian motion. Electronic J. Probab. 1 #2.
16. Lawler, G. (1996) The dimension of the frontier of planar Brownian motion. Electronic Comm. Probab. 1 #5.
17. Lawler, G. (1996) Cut points for simple random walk. Electronic J. Probab. 1 #13.
18. Lawler, G. (1998) Strict concavity of the intersection exponent for Brownian motion in two and three dimensions. Math. Phys. Electron. J. 4 #5.
19. Lawler, G. (1997) The multifractal spectrum of harmonic measure on a simple random walk path. Preprint.
20. Lawler, G. and Puckette, E. (1997) The disconnection exponent for simple random walk. Israel J. Math. 99 109-121.
21. Lawler, G. (1999) A lower bound on the growth exponent for loop-erased walk in two dimensions. ESAIM: Probab. Statist. 3 1-21.
22. Lawler, G. and Werner, W. (1999) Intersection exponents for planar Brownian motion. Ann. Probab. 27 1601-1642.
23. Lawler, G. and Werner, W. (1999) Universality for conformally invariant intersection exponents. To appear in J. European Math. Soc.
24. Schramm, O. (1999) Scaling limits of loop-erased random walks and uniform spanning trees. To appear in Israel J. Math.